Dielectric anomalies and spiral magnetic order in CoCr 2 O 4

Transcription

1 Dielectric anomalies and spiral magnetic order in CoCr 2 O 4 G. Lawes, 1 B. Melot, 2 K. Page, 2 C. Ederer, 2 M. A. Hayward, 3 Th. Proffen, 4 and R. Seshadri 2 1 Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, USA 2 Materials Department and Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA 3 Department of Chemistry, Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR, United Kingdom 4 Manuel Lujan, Jr. Neutron Scattering Center, Los Alamos National Laboratory, LANSCE-12, MS H805, Los Alamos, New Mexico 87545, USA Received 16 March 2006; revised manuscript received 25 May 2006; published 17 July 2006 We have investigated the structural, magnetic, thermodynamic, and dielectric properties of polycrystalline CoCr 2 O 4, an insulating spinel exhibiting both ferrimagnetic and spiral magnetic structures. Below T c =94 K the sample develops long-range ferrimagnetic order, and we attribute a sharp phase transition at T S 27 K to the onset of long-range spiral magnetic order. Neutron measurements confirm that the structure remains cubic at 80 K and at 11 K; the magnetic ordering by 11 K is seen to be rather complex. Density functional theory supports the view of a ferrimagnetic semiconductor with magnetic interactions consistent with noncollinear ordering. Capacitance measurements on CoCr 2 O 4 show a sharp decrease in the dielectric constant at T S, but also an anomaly showing thermal hysteresis falling between approximately T=50 and 57 K. We tentatively attribute the appearance of this higher-temperature dielectric anomaly to the development of short-range spiral magnetic order, and discuss these results in the context of utilizing dielectric spectroscopy to investigate noncollinear short-range magnetic structures. DOI: /PhysRevB PACS number s : Gg, q, Cx I. INTRODUCTION In recent years there has been renewed interest in investigating systems in which charge and spin degrees of freedom are strongly coupled. From colossal magnetoresistive materials 1 to diluted magnetic semiconductors, 2 studies on systems exhibiting an interplay between their magnetic and electronic properties have led to a deeper appreciation of the role of spin-charge coupling in determining the behavior of materials. The long-standing problem of understanding magnetodielectric coupling in insulating magnetic compounds has also been reconsidered lately. Recent results on magnetodielectrics have highlighted several important features in these systems, including the observation that incommensurate noncollinear magnetic structures tend to lead to large magnetocapacitive couplings, as does geometrical magnetic frustration. 3,4 With this background, it is natural to ask how one can use dielectric measurements to extract information about spiral spin structures in magnetic materials. CoCr 2 O 4 is a spinel ferrimagnet, with Co 2+ ions on the A sites and Cr 3+ on the B sites of the spinel structure. Both Co 2+ and Cr 3+ are magnetic; in conjunction with the fact that coupling between the B sites is also quite strong, a complex magnetic phase diagram emerges. Below approximately T c = 94 K the system has long-range ferrimagnetic order. There remain some discrepancies concerning the low-temperature magnetic phase diagram. In the original investigation on powder CoCr 2 O 4 samples, Menyuk et al. found evidence for short-range spiral magnetic order below T 86 K, and longrange spiral magnetic order below T 31 K. 5 Motivated by suggestions that ferrimagnetic spiral long-range order in CoCr 2 O 4 should be unstable, Tomiyasu et al. investigated both CoCr 2 O 4, and MnCr 2 O 4 through neutron and magnetization measurements on single crystals. 6 These more recent studies suggest that the spiral component develops incommensurate short-range order below approximately T =50 K, and that this short-range order persists to the lowest temperatures with a correlation length of only 3.1 nm at T=8 K. The authors attribute this behavior to weak geometric magnetic frustration prevalent in the spinel structure. These properties suggest that CoCr 2 O 4 would be a promising material for investigations on magnetodielectric coupling in systems with noncollinear magnetic order. CoCr 2 O 4 is insulating, and has two different types of magnetic structures ferrimagnetic and spiral. Measuring the dielectric constant in phases with both the ferrimagnetic and spiral components will offer insight into how dielectric properties couple to different magnetic structures within the same material. II. EXPERIMENTAL AND COMPUTATIONAL DETAILS Ceramic samples beautiful jade-green pellets were prepared from cobalt oxalate Co C 2 O 4 2 2H 2 O and chromium oxide Cr 2 O 3 by heating well-ground mixtures initially at 800 C for close to 24 h followed by regrinding, pelletizing, and heating at 1000 C for 24 h. The samples were initially characterized by laboratory powder x-ray diffraction Scintag X-II, Cu K radiation and then by time-of-flight powder neutron diffraction at room temperatures, 80 and 11 K at the neutron powder diffractometer 7 at the Lujan Center at Los Alamos National Laboratory. For the measurements, the samples were contained in vanadium cans. Calculations were performed using the projector augmented wave 8 method implemented in the Vienna ab-initio simulation package VASP. 9 The cubic spinel structure space group Fd3 m with the lattice parameters fixed to the experi /2006/74 2 / The American Physical Society

2 LAWES et al. FIG. 1. a Zero-field-cooled ZFC and field-cooled FC dc magnetization of CoCr 2 O 4 measured in an applied field of H =100 Oe. b Real part of the ac susceptibility of CoCr 2 O 4 measured at /2 =10 khz. Data below 40 K have been shown in an expanded view. mentally obtained a= Å was used, with an internal structural parameter for the oxygen of x = determined from the diffraction data. Different collinear magnetic structures were calculated in order to extract the Heisenberg exchange constants. The plane wave energy cutoff was 400 ev and we used an Monkhorst-Pack mesh of k points. The local density approximation LDA +U method of Dudarev et al. 10 was used and U eff was varied independently on both the Co and Cr sites. We measured the temperature and field dependence of the dc magnetization of CoCr 2 O 4 using a Quantum Design MPMS superconducting quantum interference device magnetometer, operating between T=5 and 350 K, and measured the ac magnetization of the sample on a Quantum Design physical property measurement system PPMS at frequencies between /2 =100 and 10 khz. We measured the specific heat of CoCr 2 O 4 as a function of temperature with a quasiadiabatic method on the PPMS using a 20 mg pressed powder pellet. In order to measure the dielectric constant, we pressed approximately 75 mg of CoCr 2 O 4 into a mm 3 pellet, and fashioned electrodes on opposite faces of the pellet using conducting silver epoxy. We measured the dielectric constant between /2 =1 khz and 1 MHz with an Agilent 4284A LCR meter, using the PPMS for temperature and magnetic field control. The data at lower frequencies were qualitatively similar to the higher-frequency measurements, although they were somewhat noisier and displayed larger losses, possibly due to conduction at the grain boundaries. All dielectric data presented were measured at 30 khz. III. RESULTS AND DISCUSSION FIG. 2. Time-of-flight neutron powder diffraction at a 200, b 80, and c 11 K. The symbols in each panel are data, the lines are fits using the Rietveld method to the nuclear structure, and the traces at the bottom of each panel are the difference profiles. The peaks in the difference profiles that emerge as the temperature is lowered arise from long-range magnetic ordering. Vertical lines at the top of the plot are expected positions of nuclear reflections. Crystal structure data: space group Fd3 m, a= Å at 300 K, Å at 80 K, and Å at 11 K. Co at 1/8,1/8,1/8, Cr at 1/2,1/2,1/2, and O at x,x,x with x = at all three temperatures. Figure 1 a shows the magnetization as a function of temperature measured in a 100 Oe field on warming after cooling in zero field ZFC, and while cooling in a 100 Oe field FC. The FC data are qualitatively similar to the data obtained by Tomiyasu et al. 6 on single crystals but the ZFC data show a negative magnetization at low temperatures. We attribute this to the presence of uncompensated spins at grain boundaries of our polycrystalline samples. The magnetization shows a large increase below the onset of ferrimagnetic long-range order at T c =95 K, and there is an anomaly at T S =27 K associated with spiral magnetic order in the system. It should be noted that the anomaly at T S =27 K is sharper than that presented in the Tomiyasu et al. data. 6 Figure 1 b shows the real part of the ac susceptibility of CoCr 2 O 4 acquired at a frequency of 10 khz. A very large peak in is observed at T c. The magnified trace at low temperatures shows that there is also an anomaly at at T S =27 K, consistent with the sharp anomaly in the dc magnetization measurements. Furthermore, there is another clear magnetic feature at approximately T=13 K, which is more difficult to observe in the dc measurements. Tomiyasu et al. associate this feature with a saturation of the correlation length for the spiral component on cooling. 6 These bulk magnetization measurements conclusively show the existence of magnetic features at T c =95 K and T S =27 K, associated with the ferrimagnetic and spiral magnetic structures, respectively, and a third magnetic feature at T=13 K. In order to get more information about the magnetic transitions in CoCr 2 O 4, we also conducted neutron measurements on these samples, which at this stage, can only be considered preliminary. Figure 2 displays the bank of timeof-flight neutron scattering data with largest d spacings from CoCr 2 O 4 powders. The Rietveld fits 11 to the nuclear structure

3 DIELECTRIC ANOMALIES AND SPIRAL MAGNETIC¼ FIG. 4. Specific heat measurements on CoCr 2 O 4 at H=0, plotted as C/T vs T. FIG. 3. Partial densities of Co d and Cr d states obtained for a U Co eff =U Cr eff =0 ev LSDA and b U Co eff =4 ev and U Cr eff =2 ev. Collinear Néel-type magnetic ordering was assumed. at the three temperatures are also shown. At 300 K, the data are completely fitted to the nuclear structure of this spinel compound. At 80 K, below the first collinear magnetic ordering temperature, we find that some of the peaks whose nuclear contribution are fitted have a residual intensity seen clearly in the difference spectra. This is characteristic of collinear magnetic ordering, since new peaks are not observed. At 11 K, the data reveal that the intensities of a number of peaks are not correctly fitted, as well as new reflections which have come about because of the long-range noncollinear magnetic order, again evident in the difference spectrum. While we have not at this stage been able to completely establish the magnetic structure, we present these data to strengthen our interpretation of the magnetic and transport measurements. No change in the nuclear structure is observed from the three data sets, and the spinel cell parameter changes only very little from 80 K where a = Å to 11 K where a= Å. The electronic structure of CoCr 2 O 4 was calculated using the LSDA+ U methodology. Figure 3 displays the total density of states and the partial densities of Co d and Cr d states obtained using U Co eff =U Cr eff =0 ev LSDA, top panel, as well as U Co eff =4 ev and U Cr eff =2 ev lower panel and a collinear Néel-type magnetic structure Co spins antiparallel to Cr spins. The system is an insulating fully spin-polarized ferrimagnetic semiconductor already in the LSDA, albeit with a very small gap, less than 0.1 ev. Application of U on either of the two magnetic sites enlarges the gap but only application of U on both sites leads to a significant gap of greater than 1 ev. The calculations show that this system can be expected to be a robust insulator and therefore promising for magnetodielectric measurements. We also extracted the Heisenberg exchange coupling constants by calculating the total energy differences for different collinear magnetic configurations. It has been shown by Kaplan 12 that using a simple Heisenberg model for the cubic spinel structure with only nearest-neighbor couplings J AB and J BB, the magnetic ground-state structure is determined by the parameter u= 4J BB S B / 3J AB S A, where S A and S B denote the spins of the A- and B-site cations, respectively. The collinear ferrimagnetic Néel state is the stable ground state for u u 0 =8/9, whereas for larger values of u noncollinear spiral ordering is expected. The Heisenberg exchange constants, extracted from our calculations using the reasonable values U Co eff =4 ev and U Cr eff =2 ev, are S A J AB S B =5.0 mev, S B J BB S B =2.4 mev, and u=0.65. Increasing U Co Cr eff and decreasing U eff leads to a larger value of u, eventually exceeding the critical value u 0 =8/9. In addition, we also extracted the coupling constant J AA which is neglected in the treatment of Kaplan. For the same values of U as above U Co Cr eff =4 ev and U eff =2 ev we obtain S A J AA S A =0.7 mev. This value is not necessarily negligible and indicates that the coupling between the A-site cations could play an important role in the magnetic properties of cubic spinels and in fact lead to noncollinear magnetic order even for values of u smaller than u 0 =8/9. The possible importance of A-site coupling has also been pointed out in a recent experimental study of the spinel systems MAl 2 O 4 M =Co,Fe,Mn. 13 A detailed analysis of the U dependence of the electronic structure and magnetic couplings in CoCr 2 O 4 is in progress. From the results presented in this work it can be concluded that the calculated values of the exchange coupling constants are consistent with the appearance of noncollinear magnetic order and that in addition, A-site coupling, a factor that is usually ignored, might be important in understanding the magnetic properties of this system. In an attempt to establish whether the spiral magnetic transition at T S =27 K is long range 5 or short range, 6 we measured the specific heat of our polycrystalline CoCr 2 O 4 sample on warming from base temperature. The thermodynamic data presented in Fig. 4, including both the lattice and magnetic contributions to heat capacity, strongly suggest that there are two transitions to magnetic states with long-range order, one occurring at T c =94 K and the second at T S =27 K. Specifically, the sharp peak in C/T at T S =27 K is indicative of long-range collective ordering. The development of long-range order in a polycrystalline sample which is absent in single-crystal samples 6 is unusual, but has also been observed in FeCr 2 S We can approximate the entropy under the peaks in Fig. 4 to estimate the degree of spin ordering in the long-range order at each transition. The entropy lost by CoCr 2 O 4 at T c is approximately 1 J/K per mole, while the entropy change at T S =27 K is approximately 1.5 J/K per mole, both at H=0. These changes in entropy

4 LAWES et al. FIG. 5. a Dielectric constant of CoCr 2 O 4 sample A measured at H=0 as a function of temperature. b Dielectric constant of CoCr 2 O 4 sample B measured at H=0 as a function of temperature. Vertical lines are drawn at 27 and 49 K to help locate the dielectric anomalies. All data were acquired at /2 =30 khz. are small compared to the expected change in entropy for fully spin-ordered CoCr 2 O 4 of 34.6 J/K per mole using the spin-only values for Co 2+ and Cr 3+, suggesting that these transitions involve a rearrangement of clusters of spins. This picture is consistent with the relatively large specific heat exhibited by CoCr 2 Co 4 over the entire temperature range shown, which demonstrates that significant short-range magnetic order is likely developing over a wide range of temperatures. We do not see any features in the specific heat which could be associated with a thermodynamic transition occurring at T=13 K. One of the primary motivations for these experiments was to investigate what effect the ferrimagnetic and spiral magnetic transitions would have on the dielectric constant of CoCr 2 O 4. These data are plotted in Figs. 5 a and 5 b which show the dependence of the dielectric constant on temperature for two different polycrystalline CoCr 2 O 4 samples measured on warming. In both these samples, the dielectric constant depends only weakly on temperature, with sample B showing a variation of approximately 1% over the entire temperature range, and sample A showing an even smaller change. Differences in the magnitude of the dielectric constant can be attributed to errors in determining the geometrical capacitance factor. Differences in the temperature dependence may possibly arise from small differences in conductivity between the two samples. Both samples were structurally identical verified by powder x-ray diffraction but sample B was better sintered. The general features in the dielectric constant are very similar for both these samples. Most notably, there is a welldefined drop in dielectric constant coincident with the onset of long-range spiral magnetic order at T S =27 K indicated with a vertical line. This sharp decrease is a signature of the coupling between the dielectric properties and magnetic structure, and shows no dependence on measuring frequency not plotted. The change in dielectric constant is fairly small, only 0.2% between T S =27 K and the base temperature. This should be compared with EuTiO 3 Ref. 15 and SeCuO 3 Ref. 16 which show larger changes on ordering 3.5% and 2%, respectively. The small magnitude of the shift in the dielectric constant of CoCr 2 O 4 is consistent with the idea that a small number of spin clusters order at T S,as evidenced by the thermodynamic data discussed previously. We mention that the very small change in lattice parameter between 80 and 11 K observed in neutron scattering data less than 0.02% preclude the shift from simply reflecting magnetoelastic effects. There is no clear dielectric feature at the ferrimagnetic ordering temperature T c. There may be a subtle change of slope observable in sample A, but this is not seen in sample B, which shows much larger intrinsic dependence of the dielectric constant on temperature. The lack of a sharp anomaly at T c suggests that there is at best only weak coupling between the dielectric constant of CoCr 2 O 4 and the ferrimagnetic component of the magnetic structure. Furthermore, there is no dielectric feature associated with the T = 13 K transition. Since this magnetic feature is believed to be related to the spiral magnetization component, 6 one would expect to see a clear anomaly at 13 K. However, specific heat measurements show that only a small number of spins or spin clusters are likely to be involved in this transition, which perhaps explains the absence of any dielectric feature. The dielectric constant of CoCr 2 O 4 couples only to the spiral spin structure, and not to the ferrimagnetic structure. The shift in dielectric constant observed in many magnetodielectric materials is believed to arise from strong spinphonon coupling. 15,16 Within this framework, the phonon mode giving rise to this magnetodielectric behavior must not couple to magnetic order along the 001 direction, but should be sensitive to spiral spin ordering with a propagation vector along the Q=,,0 direction in the 001 plane. 6 This observation provides an important symmetry restriction on allowed forms for the spin-lattice coupling in CoCr 2 O 4.It is known that noncollinear spin structures can break spatial inversion symmetry to obtain magnetically induced ferroelectric order in magnetoelectric multiferroics; 17,18 it is likely that breaking a spatial symmetry could also affect dielectric properties. Further investigations on the microscopic mechanisms for spin-phonon coupling in CoCr 2 O 4 will rely on a detailed understanding of the phonon modes in this system. We find evidence for one further temperature-dependent dielectric anomaly in CoCr 2 O 4. The dielectric constant shows a distinct peak at approximately T=50 K for the two samples indicated by a vertical line in Fig. 5. More precisely, measurements on sample B seem to indicate the presence of a series of peaks, while sample A rather exhibits one broader peak. The magnitude of the increase in dielectric constant at this temperature is comparable to the decrease in dielectric constant below T S =27 K. However, the origins of this feature are less clear. Neither the magnetization data in Fig. 1 nor the specific heat data in Fig. 5 show any evidence for a phase transition at this temperature. Additionally, this anomaly has a rather broad onset, which varies somewhat with sample history. Since CoCr 2 O 4 does not have any structural phase transitions at low temperatures, this anomaly must have a magnetic origin. Specifically, we believe that this dielectric anomaly arises from the onset of short-range

5 DIELECTRIC ANOMALIES AND SPIRAL MAGNETIC¼ FIG. 6. a Dielectric constant of CoCr 2 O 4 near T=50 K measured on cooling and warming at 1 K/min. b Dielectric constant of CoCr 2 O 4 near T=50 K measured on cooling and warming at 5 K/min. All data were acquired at /2 =30 khz. spiral magnetic order, which has also been shown to occur at approximately T=50 K. 6 As a further probe of this anomaly, we measured the dielectric constant on warming and cooling at different rates. At the fastest rate of 5 K/min, there is a shift of approximately 1 K in T S on warming and cooling, suggesting that there may be some small thermal decoupling. There is no such decoupling observed at a warming/cooling rate of 1 K/min. Figure 6 plots the dielectric constant of CoCr 2 O 4 measuring on warming and cooling at 1 Fig. 6 a and 5 K/min Fig. 6 b. In both cases, there is no anomaly when the dielectric constant is measured on cooling, but there is a clear feature in the dielectric constant when the sample is warmed. This thermal hysteresis may arise from a nonequilibrium distribution of regions of short-range spiral magnetic order. Furthermore, the peak temperature for this anomaly occurs at a higher temperature T=50 K when the sample is warmed at 5 K/min as compared to when it is warmed at 1 K/min T=48 K, although the thermal decoupling at 5 K/ min makes a quantitative comparison difficult. Below T S =27 K CoCr 2 O 4 develops long-range spiral order. On warming, the disappearance of a nonequilibrium distribution of spiral magnetic clusters may be responsible for the dielectric signal at T = 50 K. Conversely, when the sample is cooled from higher temperatures, there would be no spiral magnetic clusters present, and therefore no shift in the dielectric constant. In summary, we have presented extensive magnetic, thermodynamic, neutron, and dielectric data on CoCr 2 O 4. These results are consistent with a phase transition to a ferrimagnetically ordered state at T=94 K and we have conclusive evidence for a second transition to a phase with long-range spiral magnetic order below T S =27 K in our polycrystalline sample. Magnetocapacitive measurements show that the dielectric constant of CoCr 2 O 4 couples to the spiral magnetic order parameter, but is insensitive to the ferrimagnetic spin component. This limits the allowed spin-phonon coupling symmetry in this system, and places restrictions on the possible microscopic mechanism for the observed magnetodielectric shifts. Understanding magnetodielectric coupling in CoCr 2 O 4 may help illuminate the mechanisms for magnetically induced ferroelectric order in magnetoelectric multiferroics, where noncollinear spin structure is known to be an important ingredient for spin-charge coupling. 18 The dielectric constant of CoCr 2 O 4 is also found to be affected by the development of short-range spiral magnetic order. This suggests that in materials with strong spin-phonon coupling, it may be possible to use capacitive measurements to probe short-range magnetic correlations. Very recent measurements suggest that CoCr 2 O 4 is multiferroic, 19 highlighting the importance of understanding the origins of spin-charge coupling in this system. Note added in proof. Recent measurements on single crystal CoCr 2 O 4 show a peak in the heat capacity at T S, 19 consistent with long-range spiral magnetic order in these samples. ACKNOWLEDGMENTS The work at UCSB was supported by the National Science Foundation through the MRL program Grant No. DMR , and through a Chemical Bonding Center Grant No. CHE Measurements at the Lujan Center at Los Alamos Neutron Science Center were supported by the Department of Energy Office of Basic Energy Sciences and Los Alamos National Laboratory funded by Department of Energy under Contract No. W-7405-ENG-36. M.A.H. thanks the Royal Society and K.P. thanks the NSF for funding. 1 S. Jin, T. H. Tiefel, M. McCormack, R. A. Fastnacht, R. Ramesh, and L. H. Chen, Science 264, H. Ohno, Science 281, T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y. Tokura, Phys. Rev. Lett. 92, T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, Nature London 426, N. Menyuk, K. Dwight, and A. Wold, J. Phys. Paris 25, K. Tomiyasu, J. Fukunaga, and H. Suzuki, Phys. Rev. B 70, Th. Proffen, T. Egami, S. J. L. Billinge, A. K. Cheetham, D. Louca, and J. B. Parise, Appl. Phys. A: Mater. Sci. Process. 74,

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